A256670 Decimal expansion of Integral_{x=0..1} x*exp(x^3) dx.

7, 8, 1, 1, 9, 7, 0, 3, 1, 1, 0, 8, 6, 5, 5, 9, 1, 5, 1, 0, 7, 4, 3, 2, 8, 1, 4, 3, 4, 8, 2, 9, 9, 5, 0, 5, 7, 7, 6, 6, 9, 7, 3, 9, 0, 9, 6, 2, 1, 7, 8, 6, 0, 3, 9, 8, 0, 9, 2, 6, 0, 2, 6, 8, 4, 3, 2, 4, 2, 3, 4, 0, 8, 2, 2, 1, 7, 0, 4, 5, 9, 3, 2, 9, 0, 2, 4, 2, 9, 3, 5, 3, 9, 1, 5, 8, 7, 3, 3, 7, 9, 1, 3

Offset

0,1

References

Jonathan M. Borwein, Matthew P. Skerritt, An Introduction to Modern Mathematical Computing, Springer Science & Business Media, 2011, p. 89.

Links

Table of n, a(n) for n=0..102.

Formula

Equals (1/6)*(1 + i*sqrt(3))*(Gamma(2/3, -1) - Gamma(2/3)).

The simpler similar integral Integral_{x=0..1} x*exp(x^2) dx equals (e-1)/2 = 0.85914...

Example

0.7811970311086559151074328143482995057766973909621786...

Mathematica

int3 = (1/6)*(1 + I*Sqrt[3])*( Gamma[2/3, -1] - Gamma[2/3]); RealDigits[N[int3, 103] // Chop] // First

Prog

(PARI) intnum(x=0, 1, x*exp(x^3)) \\ Michel Marcus, Apr 07 2015

Crossrefs

Cf. A073006 (gamma(2/3)).

Sequence in context: A373636 A010514 A073004 * A021132 A019936 A086724

Adjacent sequences: A256667 A256668 A256669 * A256671 A256672 A256673

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 07 2015

Status

approved